be a family of probability distribution on \(\mathcal {X}\) , where each element \(p_{\mathbf {\xi }}\)  is parameterized by \(n\)  real-valued variables \(\mathbf {\xi }=(\xi ^1,\dots ,\xi ^n)\in \Xi \subset \mathbb {R}^n\) .
The set \(\mathcal {S}\)  is called a statistical model and is a subset of \(\mathcal {P}\) .
We also denote \((\mathcal {S}, g_{ij})\)  as a statistical model equipped with the Riemannian metric \(g_{ij}\) .
In particular, let \(g_{ij}\)  be the Fisher-Rao metric, which is the Riemannian metric induced from the Fisher information matrix [1]}.
